2cos (x/2 - pi/6)= корень из 3 с подробным решением

[latex]2cos( \frac{x}{2}-\frac{\pi}{6})=\sqrt3\\\\cos (\frac{x}{2}-\frac{\pi}{6} )= \frac{\sqrt3}{2} \\\\ \frac{x}{2}-\frac{\pi}{6}=\pm \frac{\pi }{6} +2\pi n,\; n\in Z\\\\ \frac{x}{2}= \frac{\pi }{6}\pm\frac{\pi}{6}+2\pi n,\; n\in Z\\\\ x=\frac{\pi}{3}\pm\frac{\pi }{3}+4\pi n, n\in Z[/latex] [latex]x= \left [ {{\frac{2\pi}{3}+4\pi n,\; n\in Z} \atop {4\pi k,\; k\in Z}} \right.[/latex] P.S.  [latex]cosx=a\; \; \to \; \; x=\pm arccosa+2\pi n,\; n\in Z[/latex]